Answer:
Option: C is the correct answer.
C. [tex]f(1)=4\\\\f(n)=5\cdot f(n-1)\ ;\ n\geq 2[/tex]
Step-by-step explanation:
Recursive Formula--
It is the formula which is used to represent the nth term of a sequence in terms of (n-1)th term of the sequence.
Here we are given a table of values by:
n f(n)
1 4
2 20
3 100
i.e. when n=1 we have:
[tex]f(1)=4[/tex]
Also,
[tex]f(2)=20\\\\i.e.\\\\f(2)=5\cdot 4\\\\i.e.\\\\f(2)=5\cdot f(1)[/tex]
Also,
[tex]f(3)=100\\\\i.e.\\\\f(3)=5\cdot 20\\\\i.e.\\\\f(3)=5\cdot f(2)[/tex]
Hence, the recursive formula is:
[tex]f(n)=5\cdot f(n-1)\ for\ n\geq 2[/tex]
